Canadian with Green Card Divorcing while in USA

First Time User:
I am a Canadian residing in Florida currently. I have been a US resident since 1996 on my second Green Card which matures in 2018. My questions are as follows:
We were married in 1986 in Canada, immigrated on my sponsorship (mother dual citizen) in 1996, we have 3 young adults, (18,19,21). We are currently residing in different states, Florida and Arizona, me solo, spouse with children.
1. Should divorce be filed in my state of residence, or country of origin?
2. Does un-sponsored spouse lose Green Card once divorced, even after 13 years of residency?
3. Should citizenship be applied for concurrently with divorce?

So your green cards were not the result of marriage based immigration, but family based, correct?

Either way, it wouldn't matter for the, as you put it "un-sponsored" spouse. Green card is a green card, and is not likely to be revoked just as a result of divorce. The requirements on the affidavit of support are met, and the sponsor is no longer responsible for any of you.

You can file for divorce in your state of residence, whichever of you is intiating the divorce.

Applying for citizenship is entirely up to you.